Write as a Vector Equality 2x+6y-4z=0 , -3x-9y+8z=0 , -x-2y+z=0

Problem

{[2*x+6*y−4*z=0],[−3*x−9*y+8*z=0],[−x−2*y+z=0])

Solution

1. Identify the coefficients of the variables x y and z in each equation of the system.

2. Express the system as a linear combination of vectors by grouping the terms associated with each variable.

3. Factor out the scalar variables x y and z from their respective column vectors.

4. Equate the sum of these scaled vectors to the zero vector to form the vector equality.

Final Answer

x*[[2],[−3],[−1]]+y*[[6],[−9],[−2]]+z*[[−4],[8],[1]]=[[0],[0],[0]]

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